Problem: Given $ m \angle MON = 6x - 24$, $ m \angle LOM = 6x + 55$, and $ m \angle LON = 115$, find $m\angle MON$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {6x + 55} + {6x - 24} = {115}$ Combine like terms: $ 12x + 31 = 115$ Subtract $31$ from both sides: $ 12x = 84$ Divide both sides by $12$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 6({7}) - 24$ Simplify: $ {m\angle MON = 42 - 24}$ So ${m\angle MON = 18}$.